The present invention relates to an objective lens system (hereinafter referred to as xe2x80x9cobjectivexe2x80x9d), in particular for a projection apparatus used in microlithography, with at least a first group of lenses or parts of lenses made of a first crystalline material and at least a second group of lenses or parts of lenses made of a second crystalline material.
Objectives of the aforementioned kind are known for example from the German patent application DE 199 29 701 A1 by the applicant of the present invention. In one embodiment, it is proposed to use calcium fluoride in parallel with barium fluoride as lens materials. In that particular embodiment, calcium fluoride takes the place of crown glass and barium fluoride takes the place of flint glass to achieve the desired achromatic lens properties.
Projection objectives in the same generic category with lenses made of two different fluoride crystals are also known from the German patent application DE 199 39 088 A1. Fluoride crystals are chosen in these cases because of their comparatively high transmissivity for wavelengths shorter than 200 nanometers. Due to the different Abbxc3xa9 numbers of the fluoride crystals used in the lenses, it is possible to achieve a chromatic correction of the projected image.
In the aforementioned references, the birefringent properties of the crystals are of no concern in the optical design of the objectives.
According to a concept known from U.S. Pat. No. 6,201,634, in the production of fluoride crystal lenses, the lens axes should ideally be aligned orthogonal to the {111} planes of the fluoride crystals in order to minimize stress-induced birefringence. However, in proposing this concept, the aforementioned U.S. Patent implicitly assumes that fluoride crystals are not intrinsically birefringent.
However, as described in the Internet publication xe2x80x9cPreliminary Determination of an Intrinsic Birefringence in CaF2xe2x80x9d by John H. Burnett, Eric L. Shirley, and Zachary H. Levine of the National Institute of Standards and Technology (NIST), Gaithersburg, Md. (posted on May 7, 2001), single crystal ingots of calcium fluoride also exhibit birefringence that is not stress-induced, i.e., intrinsic birefringence. According to the measurements presented in that study, a light ray traveling in the  less than 110 greater than  direction of the calcium fluoride crystal is subject to a birefringence that amounts to 6.5xc2x10.4 nm/cm at a wavelength of xcex=156.1 nm, to 3.6xc2x10.2 nm/cm at a wavelength of xcex=193.09 nm, and to 1.2xc2x10.1 nm/cm at a wavelength of xcex=253.65 nm. On the other hand, if the light propagation is oriented in the  less than 100 greater than  direction or in the  less than 111 greater than  direction of the crystal, no intrinsic birefringence occurs in calcium fluoride, as is also predicted by theory. Thus, the intrinsic birefringence has a strong directional dependence and increases significantly for shorter wavelengths.
Measurements made by the applicant have confirmed the intrinsic birefringence of calcium fluoride as reported by the NIST researchers, except for the wavelength of xcex=156.1 nm, where a birefringence of 11 nm/cm was measured for a ray propagating in the  less than 110 greater than  direction of the crystal.
The indices for the crystallographic directions will hereinafter be bracketed between the symbols xe2x80x9c less than xe2x80x9d and xe2x80x9c greater than xe2x80x9d, and the indices for the crystallographic planes will be bracketed between the symbols xe2x80x9c{xe2x80x9d and xe2x80x9c}xe2x80x9d. The crystallographic directions are perpendicular to the correspondingly indexed crystallographic planes. For example, the crystallographic direction  less than 100 greater than  is perpendicular to the crystallographic plane {100}. Crystals with a cubic lattice structure, which includes fluoride crystals, have the principal crystallographic directions  less than 110 greater than ,  less than {overscore (1)}10 greater than ,  less than 1{overscore (1)}0 greater than ,  less than {overscore (1)}{overscore (1)}0 greater than ,  less than 101 greater than ,  less than 10{overscore (1)} greater than ,  less than {overscore (1)}01 greater than ,  less than {overscore (1)}0{overscore (1)} greater than ,  less than 011 greater than ,  less than 0{overscore (1)}1 greater than ,  less than 01{overscore (1)} greater than ,  less than 0{overscore (1)}{overscore (1)} greater than ,  less than 111 greater than ,  less than {overscore (1)}{overscore (1)}{overscore (1)} greater than ,  less than {overscore (1)}{overscore (1)}1 greater than ,  less than {overscore (1)}1{overscore (1)} greater than ,  less than 1{overscore (1)}{overscore (1)} greater than ,  less than {overscore (1)}11 greater than ,  less than 1{overscore (1)}1 greater than ,  less than 11{overscore (1)} greater than ,  less than 100 greater than ,  less than 010 greater than ,  less than 001 greater than ,  less than {overscore (1)}00 greater than ,  less than 0{overscore (1)}0 greater than , and  less than 00{overscore (1)} greater than . Because of the symmetries of cubic crystals, the principal crystallographic directions  less than 100 greater than ,  less than 010 greater than ,  less than 001 greater than ,  less than {overscore (1)}00 greater than ,  less than 0{overscore (1)}0 greater than , and  less than 00{overscore (1)} greater than  are equivalent to each other. Therefore, those crystallographic directions that are oriented along one of the principal directions  less than 100 greater than ,  less than 010 greater than ,  less than 001 greater than ,  less than {overscore (1)}00 greater than ,  less than 0{overscore (1)}0 greater than , and  less than 00{overscore (1)} greater than  will hereinafter be identified by the prefix xe2x80x9c(100)-xe2x80x9d, and crystallographic planes that are perpendicular to these directions will also be identified by the same prefixxe2x80x9c(100)-xe2x80x9d. Furthermore, the principal directions  less than 110 greater than ,  less than {overscore (1)}10 greater than ,  less than 1{overscore (1)}0 greater than ,  less than {overscore (1)}{overscore (1)}0 greater than ,  less than 101 greater than ,  less than 10{overscore (1)} greater than ,  less than {overscore (1)}01 greater than ,  less than {overscore (1)}0{overscore (1)} greater than ,  less than 011 greater than ,  less than 0{overscore (1)}1 greater than ,  less than 01{overscore (1)} greater than , and  less than 0{overscore (1)}{overscore (1)} greater than  are likewise equivalent to each other. Therefore, those crystallographic directions that are oriented along one of the latter group of principal directions will hereinafter be identified by the prefix xe2x80x9c(110)-xe2x80x9d, and crystallographic planes that are perpendicular to these directions will also be identified by the same prefixxe2x80x9c(110)-xe2x80x9d. Finally, the principal directions  less than 111 greater than ,  less than {overscore (1)}{overscore (1)}{overscore (1)} greater than ,  less than {overscore (1)}{overscore (1)}1 greater than ,  less than {overscore (1)}1{overscore (1)} greater than ,  less than 1{overscore (1)}{overscore (1)} greater than ,  less than {overscore (1)}11 greater than ,  less than 1{overscore (1)}1 greater than ,  less than 11{overscore (1)} greater than  are also equivalent to each other. Therefore, those crystallographic directions that are oriented along one of the latter group of principal directions will hereinafter be identified by the prefix xe2x80x9c(111)-xe2x80x9d, and crystallographic planes that are perpendicular to these directions will also be identified by the same prefixxe2x80x9c(111)-xe2x80x9d. Any statements made hereinafter in regard to one of the aforementioned principal crystallographic directions should be understood to be equally applicable to the equivalent principal crystallographic directions.
The concept of rotating the orientation of lens elements in order to compensate for the effects of birefringence is described in the not pre-published patent application DE 101 23 725.1, xe2x80x9cProjektionsbelichtungsanlage der Mikrolithographie, Optisches System und Herstellverfahrenxe2x80x9d (Projection Apparatus for Microlithography, Optical System and Manufacturing Method), of the applicant of the present invention, and also in the not pre-published patent application DE 101 27 320.7, xe2x80x9cObjektiv mit Fluorid-Kristall-Linsenxe2x80x9d (Objective with Lenses Consisting of Crystalline Fluoride) of the applicant of the present invention.
The present invention has the objective to provide objectives for use in a microlithography projection apparatus, in which the influence of intrinsic birefringence of the crystalline lens material is significantly reduced.
The invention meets the foregoing objective by providing an objective, in particular for a projection apparatus used in a microlithography, with at least a first group of lenses or parts of lenses made of a first crystalline material and at least a second group of lenses or parts of lenses made of a second crystalline material. Due to the birefringent properties of the lens materials and depending on the specific configurations of the first and second groups of lenses, a light ray traversing the first lens group is subject to a first optical path difference between two mutually orthogonal states of linear polarization, while the same light ray is subject to a second optical path difference in the second group. The objective according to the present invention is designed so that in particular for a peripheral light ray (i.e., a ray traversing the border area of the lens aperture, which hereinafter will also be referred to as an outermost aperture ray) the first and second optical path differences will approximately compensate each other.
According to a preferred embodiment of the invention, the lenses or parts of lenses of the first group consist of calcium fluoride, while the lenses or parts of lenses of the second group consist of barium fluoride.
Under a more specifically defined concept of the preceding embodiment, the central axes of the lenses or lens parts of the two groups are aligned approximately along the same or equivalent principal crystallographic directions and, furthermore, equivalent principal crystallographic directions of the lenses or lens parts of the two groups are aligned approximately in the same directions.
The scope of the present invention includes a microlithography projection apparatus with an illumination system and with an objective as described above, which projects an image of a mask structure onto a light-sensitive substrate. Further included in the scope of the invention is a method of producing semiconductor elements by means of the inventive microlithography projection apparatus.
Finally, the invention also covers a method of manufacturing a lens by seamlessly joining a first plate made of a first crystalline material and a second plate made of a second crystalline material, where the seamless joint is achieved in particular by a so-called wringing fit, i.e., the mating between ultra-flat surfaces that will adhere to each other by molecular attraction without the use of a bonding agent. Subsequently, the joined plates are subjected to shaping and polishing operations. Due to the birefringent properties of the crystalline plates, a light ray traversing the first plate is subject to a first optical path difference between two mutually orthogonal states of linear polarization, while the same peripheral light ray is subject to a second optical path difference in the second plate. The inventive method is further characterized by the fact that the first and second optical path differences will approximately compensate each other.
In a specific embodiment of the method described in the preceding paragraph, the first plate consists of calcium fluoride and the second plate consists of barium fluoride.
Advantageous further developments and specific features of the aforedescribed embodiments of the invention may be learned from the following description as well as the attached drawings.
According to the invention, the effects of the intrinsic birefringence are minimized by using an objective that has at least two groups of lenses or lens parts. The lenses or lens parts (also collectively referred to as optical elements) of a given group are made of the same crystalline material, while the lenses or lens parts of different groups are made of different crystalline materials. A group, as the term is used herein, can be made up of one individual lens or a plurality of lenses, or also of an individual lens part or a plurality of lens parts. The term xe2x80x9clens partsxe2x80x9d is used to describe, for example, individual lenses that are seamlessly joined by the above described wringing fit to form one unitary lens. In the most general sense, the term xe2x80x9clens partsxe2x80x9d refers to the parts of an individual lens, where the lens axes of the lens parts are aligned in the direction of the lens axis of the individual lens. The lens materials are selected and the lenses or lens parts are designed and arranged in such a manner that an outermost aperture ray is subject to a significantly reduced optical path difference between two mutually orthogonal states of linear polarization. The overall optical path difference for the objective is represented by the sum of a first optical path difference and a second optical path difference occurring in the aperture ray while traveling through the first and second groups, respectively. The detrimental influence of the birefringence phenomenon is considered to be significantly reduced if the combined optical path difference is smaller than 30%, and particularly significant if it is smaller than 20% of the maximum value of either of the two separate path differences. The term xe2x80x9coutermost aperture rayxe2x80x9d refers to a light ray that traverses a diaphragm plane of the objective at a distance from the lens axis that is equal to the aperture radius of the diaphragm, so that on the image side of the objective, the ray encloses an angle with the lens axis that corresponds to the numerical aperture. The outermost aperture rays are used to characterize the inventive concept, because they normally have the largest aperture angles in relation to the lens axes and therefore suffer the most from the undesirable effects of the birefringence phenomenon.
The lenses can be, for example, refractive or diffractive lenses as well as correcting plates with free-form surface shapes. Planar-parallel plates, too, are considered as lenses if they are arranged in the light path of the objective.
The invention can be used to good advantage in projection objectives for a microlithography projection apparatus, because this application poses extremely exacting requirements on the resolution of the projection objective. The birefringence phenomenon also affects lens-testing objectives that are used to test lenses for projection objectives by measuring wave fronts of large aperture. Thus, a birefringence compensation is desirable for lens-testing objectives, too. Further possible applications exist in objectives that are used to inspect integrated circuit wafers, as well as in microscope objectives, and in objectives for illumination systems that are used to illuminate the objects that are projected or viewed with the aforementioned types of objectives.
Particularly for lenses used at wavelengths shorter than 250 nanometers, fluoride crystals such as, e.g., calcium fluoride, barium fluoride, or strontium fluoride have been found to be advantageous as lens materials.
It is a known property of calcium fluoride that it exhibits an angle-dependent intrinsic birefringence. According to measurements performed by the applicant of the present invention, a value of 11 nm/cm for the wavelength of xcex=156.1 nm was found for the birefringence in a light ray traveling in the direction (110) of the crystal. Similar measurements in barium fluoride have shown that the latter, likewise, exhibits intrinsic birefringence with a comparable dependence on angular orientation, which is explained by the fact that calcium fluoride and barium fluoride belong to the same type of crystals. The measurements of birefringence performed by the applicant in barium fluoride with a ray propagating in the (110)-direction of the crystal resulted in a birefringence value of 25 nm/cm for the wavelength of xcex=156.1 nm. However, it should be noted that the birefringence effect is characterized not only by its numerical amount, but also by its direction. The direction of the birefringence is defined as the direction of the so-called slow axis. For linearly polarized light, the index of refraction is greatest if the polarization is oriented in the direction of the slow axis. The inventors recognized that the axes of birefringence for light traveling in the (110)-direction of calcium fluoride and barium fluoride are orthogonal to each other, so that a light ray propagating in the (110)-direction is subject to travel path differences of opposite signs in calcium fluoride and barium fluoride for two mutually orthogonal states of polarization. This property is advantageously exploited in the present invention to achieve a reduction of the unwanted influence of the birefringence phenomenon. Through the combination of lenses or lens parts of different crystalline materials that produce light-path differences of opposite sign for two mutually orthogonal states of linear polarization in a polarized light ray, and through an optical design that is determined by the birefringent properties, it is possible to achieve at least an approximate compensation of the unwanted effects of birefringence that occur when only one crystalline material is used.
The compensation is particularly successful if the lens axes of all of the lenses or lens parts are oriented along the same principal crystallographic direction or along equivalent crystallographic directions. The lens axis may coincide, e.g., with the symmetry axis of a rotationally symmetric lens. If the lens does not have a symmetry axis, the lens axis may be defined as the centerline of an incident bundle of light rays, or as that line in respect to which the ray angles of all light rays within the lens are minimal. The lens axis of a planar-parallel plate is perpendicular to the planar lens surfaces. The lens axes are considered to coincide approximately with a principal crystallographic direction if the maximum deviation between lens axis and principal crystallographic direction is less than 5xc2x0. It is of advantage if the first and second crystalline materials belong to the same crystal type and the lens axes are oriented approximately in the same principal crystallographic direction, because the magnitudes of the birefringence effect will be distributed similarly in the lenses or lens parts. The distribution functions xcex94n(xcex1L,xcex8L) in this case are given as a function of the aperture angle xcex8L and of the azimuth angle xcex1L. The aperture angle xcex8L represents the angle that a light ray encloses with the lens axis, while the azimuth angle xcex1L represents the angle between the projection of the light ray into a plane perpendicular to the lens axis and a fixed reference direction that runs in the same perpendicular plane and is tied to the lens.
The value of the birefringence function xcex94n is equal to the difference between the refractive indices for the so-called slow axis and the so-called fast axis of two mutually orthogonal states of linear polarization of a light ray traveling in the direction defined by the aperture angle xcex8L and the azimuth angle xcex1L. Thus, the birefringence index xcex94n represents the quotient of the optical path difference (in nanometers) divided by the length (in centimeters) of the physical light path inside the fluoride crystal. The intrinsic birefringence is dependent on the paths of the light rays and on the shape of the lens. According to the foregoing definition of xcex94n, the optical path difference is obtained by multiplying the birefringence index xcex94n with the path length traveled by the ray inside the birefringent medium.
In cases where the birefringent properties occur, e.g., as a result of the manufacturing process of the fluoride crystal or as a result of mechanical forces acting on the lens (stress-induced birefringence), it is of course understood that the inventive problem solutions disclosed herein can likewise be used to achieve a reduction of the harmful influence of the birefringence phenomenon.
It is advantageous if the lens axes of the lenses and lens parts of the two groups are oriented along the crystallographic directions (100) or (111). The birefringence function xcex94n vanishes at the aperture angle xcex8L=0xc2x0. The values of xcex94n increase with increasing aperture angles. The distribution pattern of xcex94n exhibits fourfold azimuthal symmetry if the lens axis is oriented in the crystallographic direction (100), and threefold azimuthal symmetry if the lens axis is oriented in the crystallographic direction (111). This means that for a given fixed aperture angle xcex8O the birefringence distribution xcex94n(xcex1L, xcex8O) will have four local maxima and minima if the lens axis is oriented in the crystallographic direction (100), and three local maxima and minima if the lens axis is oriented in the crystallographic direction (111). This applies to calcium fluoride as well as to barium fluoride.
It is particularly advantageous if equivalent principal crystallographic directions are oriented in approximately equal directions for the lenses or lens parts of the at least two groups, so that the maximum deviations are smaller than 10xc2x0 between corresponding principal crystallographic directions. Thus, the lenses or lens parts of the first and second groups will have approximately the same crystallographic orientation.
Although the largest aperture angles in projection lenses occur typically for the outermost aperture rays, it is also conceivable to compensate the optical path differences for two mutually orthogonal states of linear polarization for other rays, such as for example principal rays (i.e., rays traversing the center of a diaphragm plane), by using two groups of lenses or lens parts made of two different crystalline materials whose birefringent behaviors are complementary, such as for example barium fluoride and calcium fluoride. If one considers pupil imaging instead of field imaging, the outermost aperture ray will be equivalent to the principal ray with the largest object height, because this principal ray has the same ray height (perpendicular distance from the lens axis) in the object plane as the border of the object field. Therefore, the present observations which relate to the outermost aperture rays can also be applied to the compensation of the optical path differences for the outermost principal rays.
The detrimental influence of birefringence for the outermost aperture rays will be significantly reduced, if the reference directions of the individual lenses or lens parts of the two groups are oriented in such a way that the birefringence distribution functions run conjugate to each other, and if the lenses or lens parts are rotated about their lens axes in such a manner that the reference directions are aligned with a deviation of no more than 10xc2x0. Two birefringence distribution functions are said to run conjugate to each other, if the local minima of the birefringence values occur approximately at the same azimuth angles. With this arrangement of the lenses, the respective azimuthal sectors of maximum and minimum birefringence occur at the same azimuth angles relative to a fixed reference direction that is tied, for example to the image plane. For a bundle of rays falling on an image point in the image plane of the objective, the distribution of the optical path differences for two mutually orthogonal states of linear polarization is thus nearly independent of the azimuth angle of the rays.
In the arrangement just described, it is sufficient if the first group consists of only an individual lens or a part of an individual lens and the second group, likewise, consists of only an individual lens or a part of an individual lens. The thicknesses and radii of the lenses should be chosen to achieve approximately opposite path differences in the two lenses or lens parts for two mutually orthogonal states of linear polarization in the outermost aperture ray.
The detrimental influence of the birefringence effect can also be compensated with an arrangement where the two groups with the different crystalline materials each have at least two lenses or lens parts, that are oriented within their groups in a rotated position about the lens axis. As the birefringence distribution functions of the lenses are dependent on the azimuth angle, the rotated arrangement will reduce the maximum value of the optical path differences by 20%-25% in comparison to the non-rotated-arrangement of the lenses in a group for a bundle of rays falling on a point in the image plane.
In particular, with the rotated arrangement of the lenses or lens parts within the group, the distribution of the optical path differences caused by the group can be made less dependent on the azimuth angles of the rays of the bundle, so that the distribution function will be nearly symmetric relative to azimuthal rotation. The azimuth angle of each ray is defined as the angle between the projection of the ray into the image plane and a fixed reference direction in the image plane. Finally, by combining the two groups that are made of different crystalline materials, the nearly symmetric respective distributions of optical path differences in the first and second group will compensate each other.
If the reference directions are oriented in such a manner that the birefringence distributions run conjugate to each other, it is advantageous to set the angle of rotation xcex3 between two reference directions of lenses or lens parts of a group as follows:   Y  =                    360        ⁢        xc2x0                    k        ·        n              +                  m        ·                              360            ⁢            xc2x0                    k                    ±              10        ⁢        xc2x0            
In this equation, k stands for the degree of azimuthal symmetry, n for the number of lenses in a group, and m of an arbitrary integer number. The tolerance of xc2x110xc2x0 allows for the fact that the angles of rotation may deviate from the theoretically ideal angles, so that other constraints can be taken into account in the fine adjustment of the objective. A deviation from the ideal angle of rotation leads to non-optimized azimuthal compensation of the optical path differences of the lenses in a group. This can, however, be tolerated within certain limits.
For lenses or lens parts whose lens axes are oriented in the crystallographic direction (100), the angles of rotation according to the foregoing equation are determined as:   Y  =                    90        ⁢        xc2x0            n        +                            m          ·          90                ⁢        xc2x0            ±              10        ⁢        xc2x0            
If the group is made up of two lenses with (100)-orientation, the angle of rotation between the two lenses will ideally be 45xc2x0 or 135xc2x0, 225xc2x0, . . . etc.
Analogously, for lenses or lens parts whose lens axes are oriented in the crystallographic direction (111), the equation angles of rotation are determined as:   Y  =                    120        ⁢        xc2x0            n        +                            m          ·          120                ⁢        xc2x0            ±              10        ⁢        xc2x0            
If the outermost aperture ray has similar aperture angles in the lenses or lens parts of the two groups, it is advantageous to adapt the thicknesses and radii of the lenses to the birefringent properties of the crystalline material, among other considerations. The birefringence effect in calcium fluoride and barium fluoride is greatest in the crystallographic direction (110). Thus, the birefringence value for light propagating in the (110) direction represents the reference quantity. To achieve an optimum of compensation of the two groups, the ratio between the respective path lengths of a ray in the first and second group should be approximately the reciprocal of the ratio between the respective birefringence values of the first and second crystalline materials in the crystallographic direction (110). The light path of a ray in a group equals the sum of the light paths for that ray in the individual lenses or lens parts of the group. A good degree of compensation is achieved in an arrangement where for similar aperture angles within the lenses or lens parts of the two groups, with a variation of less than 20% relative to the maximum aperture angle, the quotient of the ratio between the respective light paths for a ray in the first and second group divided by the reciprocal ratio of the respective birefringence values of the crystal materials relative to the (110)-direction lies in a range between 0.8 and 1.2.
The detrimental influence of birefringence is reduced with particular effectiveness if the two groups are arranged adjacent to each other, because in this case the rays of a bundle will have similar azimuth angles in the two groups. In particular, the lens parts of two groups can be seamlessly joined, e.g., by wringing. This produces an individual lens that has two groups of lens parts.
A determining factor for the lenses of a group is for example that an outermost aperture ray of a bundle of rays has similar aperture angles within the lenses of the group. Advantageously, the aperture angle of the outermost aperture ray within these lenses is larger than 20xc2x0 and, more particularly, larger than 25xc2x0. These large aperture angles are found in objectives with large numerical apertures on the image side, exceeding in particular a value of 0.7, so that compensation measures are necessary to reduce the detrimental influence of birefringence.
Large aperture angles in lenses occur mainly in the proximity of field planes, particularly in the proximity of the image plane. The groups provided for the compensation should therefore preferably be arranged in the proximity of the field planes. Ideally, one of the two groups includes the lens closest to the image plane.
The magnitude of the intrinsic birefringence increases noticeably when working with shorter wavelengths. For example in comparison to a wavelength of 248 nm, the intrinsic birefringence is more than twice as large at a wavelength of 193 nm, and more than five times as large at a wavelength of 157 nm. The present invention is therefore used with particular advantage for light with a wavelength shorter than 200 nm, and in particular shorter than 160 nm.
Objectives of the kind proposed by the present invention are used advantageously as projection objectives in microlithography projection apparatus which include a light source, an illumination system, a mask-positioning system with a mask carrying a structure, the projection objective, and an object-positioning system to hold a light-sensitive substrate. In this projection apparatus, the objective projects an image of the mask structure onto the light-sensitive substrate.
The microlithography apparatus of the foregoing description serves to manufacture micro-structured semiconductor components.
The scope of the invention also includes a method of manufacturing a lens. In a first step of the method, a first plate and at least one second plate are seamlessly joined to form a blank, and in a second step the lens is formed from the blank by known production methods. The first and second plates consist of different crystalline materials. The crystalline materials, the crystallographic orientations, and the plate thicknesses are selected so that for a light ray that is subject in the first plate to a first optical path difference between two mutually orthogonal state of linear polarization, and in the second plate to a second optical path difference between two mutually orthogonal state of linear polarization, the first and second optical path difference approximately compensate each other, so that the resultant optical path difference is less than 30%, and in particular less than 20%, of the maximum amount of either of the individual optical path differences.
A very good compensation is obtained, e.g., with calcium fluoride and barium fluoride as crystal materials, because they have similar birefringent properties, while at the same time, their directions of birefringence in the crystallographic direction (110) are orthogonal to each other.
It is advantageous if the directions perpendicular to the first and second plates (also referred to as normal vectors of the plates) are oriented approximately in the same principal crystallographic direction or in equivalent principal crystallographic directions. The deviation from the principal crystallographic direction should not exceed a limit of about 5xc2x0.
The crystallographic direction (100) and (111) are advantageous as directions for the normal vectors of the plate surfaces, because the birefringence effect vanishes for light rays in these exact directions.
A good degree of compensation for the two plates is achieved if the equivalent crystallographic directions are oriented in approximately equal directions for the first and second plates, i.e., if the crystals have the same orientation. Deviations up to about 10xc2x0 can be tolerated.
Near-perfect compensation is achieved if, in addition, the thicknesses of the first and second plates are suitably adapted. The deciding factor for the plate thicknesses lies in the respective magnitudes of the birefringence indices for the first and second crystalline materials in the crystallographic direction (110). The ratio between the thickness of the first plate and the thickness of the second plate should be approximately the reciprocal of the ratio between the first and second birefringence index. The deviation between the aforementioned ratio and reciprocal ratio should be no more than 20% of the maximum value of the two ratios.
The lens-manufacturing method of the foregoing description can be used to produce lenses for applications in objectives, particularly in projection objectives used in microlithography.